Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta

Abstract

Algorithms are developed for the exact evaluation of the 3j‐coefficients of Wigner and the 6j‐coefficients of Racah. These coefficients arise in the quantum theory of coupling of angular momenta. The method is based on the exact solution of recursion relations in a particular order designed to guarantee numerical stability even for large quantum numbers. The algorithm is more efficient and accurate than those based on explicit summations, particularly in the commonly arising case in which a whole set of related coefficients is needed.